Apply the product rule:
; to find :
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
; to find :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result of the chain rule is:
The result is:
The answer is:
6*sin(2*x) + 12*x*cos(2*x)
24*(-x*sin(2*x) + cos(2*x))